Abstract
We draw some connections between Nash's theorem on imbedding of Riemannian manifolds and E (∞) space and speculate on further connections to fractal spacetime and high energy physics. It is conjectured that 26 dimensions are required for imbedding a Menger sponge of arbitrary large size into an arbitrary small portion of the 26 dimensional space. We further conjecture that the 26 dimensions on their own already imply the fracticality of the surfaces imbedded into such a space and allow for a non-intuitive results similar to the Banach–Tarski decomposition theorem.
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